The Belgian scored a fine header after 81 minutes to give his side a 2-1 victory over the Gunners.
And Alderweireld says the performance was a result of Tottenham's hard work on the training pitch.
"It was a good cross, I thought it was a little bit too high and I got my head underneath it. It was a nice goal," the Spurs centre-back told BBC Radio 5 Live.
"It always [hurts after defeat], people don't see how hard we work. We tried to do better today and showed there is character in the team, like fighting spirit.
"Defensively we are getting much better in the last couple of games and you have seen we have quality up front because we could have scored more than two goals.
"Sometimes you need some confidence, like a good win and get the momentum a little bit. The only thing we can do is work hard. What people don't see is that everyone is putting everything into it and I believe that things will change. Today is a very important win for us and the fans."